Further results on delay-dependent stability for continuous system with two additive time-varying delay components

- A continuous system with two additive time-varying delay components is concerned.
- A novel Lyapunov-Krasovskii functional is constructed.
- A delay-dependent stability criterion has been obtained by using the method of reciprocal convex and convex polyhedron.
- This criterion is expressed as a set of linear matrix inequalities.

This paper deals with the problem of stability for continuous system with two additive time-varying delay components. By making full use of the information of the marginally delayed state, a novel Lyapunov-Krasovskii functional is constructed. When estimating the derivative of the Lyapunov-Krasovskii functional, we manage to get a fairly tighter upper bound by using the method of reciprocal convex and convex polyhedron. The obtained delay-dependent stability results are less conservative than some existing ones via numerical example comparisons. In addition, this criterion is expressed as a set of linear matrix inequalities, which can be readily tested by using the Matlab LMI toolbox. Finally, four examples are given to illustrate the effectiveness of the proposed method.